2014-11-28

The meaning of Get together'': Part 3

I like to make a quiz like in the last article. But some of my friends said to me Many can live without knowing such things.'' That would be true. I even thought that it is natural that many people don't care about that. But recently I found some people deceive others by using this kind of wrong math. I feel sad when the honest people were deceived. Especially when I read a newspaper article that someone used this kind of wrong logic and stole some money from people. I think it may be good to know these kind of things not to be deceived by malicious people.

The problem here is actually not exactly a mathematical problem, it is rather a language problem. If you understand the meaning of the problem, actually this is not so much math in there.

Since the question is described in a language (originally in Japanese, here in English. I found it is interesting this worked for both languages), we need to understand what the problem means. Here we need to know what is the 'goal success ratio' and what does 'get together' means. I wanted to him to think about these words really means. A goal success ratio is actually simple. It is the ratio of how many shoots were tried and how many goals were succeeded. But I didn't realized for a long time, I found people actually don't think about what is 'get together' means. When I found this, I made this problem. Here I made up an expression that adds two numbers together, but the result doesn't change. This is a strange calculation, isn't it? I use the double meanings of the 'get together' to make this happen.

I coincidentally find that the words 'get together' is actually not a simple expression. Language is a deep subject. The phrase is used so often, we are just too familiar with that. But sometimes I can find something so familiar, thus I thought I knew it well, but I actually didn't know about it. Maybe similar things happens with a person. I think I know someone well, but one day I realized I didn't know that person well... This is a blind spot. If you learn literature, you may deeply think of each word you are using. However it is hard to do in the everyday life. But if you don't realized what is wrong here, that means you may think that adding non-zero numbers don't change the amount. Someone could use this method as a fee calculation or a tax calculation. It seems you didn't pay much at the amount, but you actually pay a lot. I don't want to people are deceived by this kind of wrong logic. Since I am living in a democratic country, if many people are deceived, I will also deceived. Actually I am forced to be deceived. That's democracy.

This boy understood the meaning of the question. And he found my lie. Then, he asked me, Does a teacher lie?'' This was an excellent question. I answered, Of course! A teacher would lie. But, most of the cases, a teacher actually doesn't lie, but a teacher may make a mistake. If you could find that by thinking yourself, I am really glad.'' (I also hope he has a good communication skill since I had a lot of trouble of lacking the skill.)

Any authority, like a teacher, might lie and might make a mistake. Many of my generation knows words: We, adults, don't lie on purpose, but we make mistakes.'' when a famous cartoonist in Japan made a fatal mistake in his story. The boy realized it. I wish he continues to try to understand the world himself, not just following the authority. I just teach him one method to think himself through mathematics. We could also think through learning literature, or foreign languages, and so on. But I think it is a good start. I am so glad he found this by himself.

Nowadays, our life is deeply based on science. Thus I believe there is a basic science knowledge we, all the citizen, should know about it. In many countries, everyone needs to learn some science in the elementally school. I think this is not for making everyone scientists. We need to know the infrastructure of our society. For instance, we cannot completely ignore where the electricity comes from. It may affect the environment, and I recall the Fukushima incident. We should know some concept of computer security, otherwise we cannot safely buy anything through the internet. I believe we all need some basic knowledge about math and science in our society. I will be happy if my article is one of the clues for someone who later become curious to science or mathematics.

In this article, I didn't exactly explain what is the problem in the question. But 13 year-old boy can find it. I also put some hints in the article, so I hope you think through the problem. Please don't search it immediately. Let's think first before searching the answer on the internet.

2014-11-26

The meaning of Get together'': Part 2

A while ago, I taught mathematics to a thirteen years old boy. His family moved to another city, so we could not have more sessions, but I liked to teach him.

In the last session, we discussed about addition of fractions. If we get a half cake ($$\frac{1}{2}$$) and a half cake ($$\frac{1}{2}$$) together,
\begin{eqnarray*}
\frac{1}{2} + \frac{1}{2} = \frac{1+1}{2} = \frac{2}{2} = 1,
\end{eqnarray*}
it becomes 1. If we add fractions with like denominators, we only add numerators. We discussed why we did in this way and what this meant.

Then I told him a story. The boy's favorite soccer player tried to shoot the goal twice in a game, and he succeeded once. His goal ratio of this game is $$\frac{1}{2}$$. (Two shoots, one goal) The next game, again he tried to shoot the goal twice in the game, and again he succeeded once. His goal ratio of the game is again $$\frac{1}{2}$$. Let's think about his goal ratio to get two games together. For these two games, he tried four goals in total, but succeeded twice in total. Therefore, his total goal ratio is:
\begin{eqnarray*}
\frac{1}{2} + \frac{1}{2} = \frac{1+1}{2+2} = \frac{2}{4} = \frac{1}{2}.
\end{eqnarray*}
The goal success ratio is correct. However, how is $$\frac{1}{2}$$ + $$\frac{1}{2}$$ equal to $$\frac{1}{2}$$. That must be 1. This also violated the rule of fraction addition. If we got two $$\frac{1}{2}$$ cakes together,
\begin{eqnarray*}
\frac{1}{2} + \frac{1}{2} = 1,
\end{eqnarray*}
but, when we got two games goal ratio together,
\begin{eqnarray*}
\frac{1}{2} + \frac{1}{2} = \frac{1}{2}.
\end{eqnarray*}
I asked him why this happened. It is quite strange that one addition expression has two different answers. 1+1 is only equal to 2. There should not be two different answers of one addition, like 1 + 1 = 2 and 1 + 2 = 1 at the same time. Therefore, at least one should be wrong.

We discussed this problem. He first told me the total goal ratio must be 1 as the cake's addition. But I added one more game, the player tried two goals and one success, then in total three games,
\begin{eqnarray*}
\frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{3}{2}.
\end{eqnarray*}
Now the goal success ratio is $$\frac{3}{2}$$. This means this player tried two kicks and he got three points. How it could be possible? At that time, his father just passed by us, and made a joke, He is the best player, he could get three points with two shoots.'' But we all know that is not possible, so something wrong in this calculation. When we want to get all the three games together, his goal ratio should be
\begin{eqnarray*}
\frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{1+1+1}{2+2+2} =
\frac{3}{6} = \frac{1}{2}.
\end{eqnarray*}
Since he always success one goal per two shoots. In other words, he tried six shoots and succeeded three goals, this means his goal success ratio is $$\frac{3}{6}$$ which is $$\frac{1}{2}$$.

Our discussion continued more than 20 minutes, but at the end, he found what is the problem. Why this strange thing happens. I was impressed. It was a great moment for me and hopefully also for him.

The following article will be the conclusion of this story.

2014-11-25

The meaning of Get together'': Part 1

Every person thinks by words. Thus words are important for me, too. Especially I need to write programs to realize an idea through the words. We can easily find that one word has sometimes a few meanings. People make a joke from it. I think one word has a few meaning is quite natural. For instance, run'' has a few meaning. I run as I move fast by foot. I can run a shop. A movie is now running at the theater. In English, it has more meanings with a short word (run after, run away, run out, ...), however, you have already seen the run'' itself has a few meanings.

When we used only one language, we hardly noticed this multiple meaning of a word. However, when we learn foreign languages, we need to notice this through the translation. We can easily see one word usually has more than one translation in a dictionary. When we learn a foreign language, we can usually see the deepness of both our own language and the foreign language. In literature, especially in poems, using the double meaning of word is important. In the book 1984, Orwell describes Newspeak to restrict the people's ideas by eliminating the double meaning of the words. If you learn a modern computer language, you'll find some of the languages have a concept overloading.'' One name can have a few implementations. This is an adaptation to the human being uses the same word, but different meanings. If you learn mathematics, you can also notice some operators have different meaning depends on the context.

I sometimes feel the literature and mathematics share a common concept. Some people (e.g., Lewis Carroll, Noam Chomsky, ...) are good at both literature and mathematics. I would imagine they might also feel this common concept.

I sometimes feel that thinking about what I am really saying, is important since one word can have a few different meanings. I recently have an experience about this, so I will write it in the next blog article.

2014-11-11

Frontline Volunteer

My closest person offered him a volunteer to fight Ebola. He is just a programmer and neither a doctor nor a nurse, so I wonder what he can do for that. However, the frontline people need not only doctors and nurses, but also support people. He found a position of IT, the frontline people will establish a data center for outbreak and information hub.

I asked him, Don't you have a fear to do that?'' He answered me, I'm scared.'' The Ebola has a high risk of death, 50 to 90% of death ratio once infected. There is no good medicine for it yet.

But he thought, the outbreak must be stopped there and must be stopped still we can. He told me he doesn't have any family, so he just felt that he does it better than someone who has a family does. Although he clearly sees what he should do, still his hand was trembled when he pushed the send'' button of the application form.

For one week just after he sent the form, he continue to think about what he should do before he go. His hobby is making introductory math videos for children. He just continued to make them. He told me it was a quite productive one week. But I know the work is never done in a week, so I wonder it is good thing to do or not. He seems to feel what I am thinking, he told me that, I could not find any other things I need to do now.'' He also tried to find some medical training that he could do in Berlin. But, it is not so simple.

One and half a week later, he got a letter: This time the frontline allies are not expressing an interest in volunteers with his skills, profile, and availability. But the frontline situation is always changing, if the frontline needs him, they will let him know right away. I think his specialty is only for computer and maybe the frontline people need the people who know more about medical stuffs. He didn't talk about this anyone until he got this letter.

He told me that that one and half week was a special week for him. He had a strange feeling. He thought If I could not come back here again....'', but he also thought What do I want to do even I could come back?... I have nothing special.'' Then he realized that it makes much sense he helps to stop the disease.

But, he made one plan, he thought it might be the last plan. His friend's child will have a birthday at 18th of November. He bought a ticket to Dresden and he wanted to celebrate her birthday before he leaves.

Gap time volunteer: Lunch break volunteer version

I call a fraction time Gap time''. A gap time is for instance, a time I am waiting for my next train, a time I am waiting for someone at a cafe, my commute time, and so on. Everyday I have some fraction time that I need to wait something a bit. I have a volunteer work for translating education materials. I often use this gap time'' for it.

I'm a lazy person, therefore I could hardly find some amount of continuous time for my volunteer work. I believe if I work hard, I cannot continue it. Thus my strategy is don't work hard, do just small amount only, but continue everyday for long time.''

I translate Khan Academy learning materials and its site to Japanese and German. I could translate English to Japanese alone, but I need some help for German translation. I ask to help for this at the lunch break gap time. When I and my colleagues go to lunch, I ask someone to proofread my translation while we are waiting for our coffee. This is a lunch break volunteer.

I translate one or two math exercise problems almost every day. I printed it out and bring it to our lunch. We often go to our favorite coffee house after the lunch, I ask one of my colleagues to proofread my translation at there. One of six colleagues help me out at once. Here is a snapshot picture of how it looks like. The pictures below are an example of proofreading and some of them.

 Lunch break volunteer snapshot